write a quadratic functions for graph that has an axis of symmetry of x= -3/2.
summarize your steps.
To write a quadratic function with an axis of symmetry of x = -3/2, we need to consider the general form of a quadratic function, which is in the form of f(x) = ax^2 + bx + c.
The axis of symmetry for a quadratic function is given by the formula x = -b/2a. In this case, we already have the axis of symmetry, x = -3/2, which means that -b/2a = -3/2.
To find the correct values of a and b for the quadratic function, we can follow these steps:
Step 1: Substitute x = -3/2 into the equation -b/2a = -3/2.
Step 2: Solve for b:
-b/2a = -3/2
Multiply both sides by 2 to eliminate fractions:
-b = -3
Divide both sides by -1 to solve for b:
b = 3
Step 3: Now that we know the value of b, we can substitute it back into the quadratic function equation:
f(x) = ax^2 + bx + c
f(x) = ax^2 + 3x + c
Step 4: To find the value of a, we need another piece of information, such as a point on the graph. Without additional information, we cannot determine a unique quadratic function that satisfies both the axis of symmetry and a specific point on the graph.
So, without more information, the quadratic function with an axis of symmetry of x = -3/2 can be represented as f(x) = ax^2 + 3x + c, where a is unknown without additional information.